Combining Texts

All the ideas for 'Defending the Axioms', 'Confessio naturae contra atheistas' and 'Logical Atomism'

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22 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
6118 Philosophy is logical analysis, followed by synthesis [Russell]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
6116 A logical language would show up the fallacy of inferring reality from ordinary language [Russell]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
6117 Philosophy should be built on science, to reduce error [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
6110 Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6107 It is logic, not metaphysics, that is fundamental to philosophy [Russell]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
6115 Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
6109 Some axioms may only become accepted when they lead to obvious conclusions [Russell]
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
6108 Maths can be deduced from logical axioms and the logic of relations [Russell]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
10968 Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read]
6113 To mean facts we assert them; to mean simples we name them [Russell]
6114 'Simples' are not experienced, but are inferred at the limits of analysis [Russell]
21722 Better to construct from what is known, than to infer what is unknown [Russell]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
6111 As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell]
9. Objects / A. Existence of Objects / 5. Individuation / c. Individuation by location
12693 A body is that which exists in space [Leibniz]
19. Language / A. Nature of Meaning / 1. Meaning
6112 Meaning takes many different forms, depending on different logical types [Russell]